Abstract

Multipoint iterative methods with memory are the class of the most efficient iterative methods for solving nonlinear equations since they use already computed information to considerable increase convergence rate without additional computational costs. The purpose of this study is to provide an overview about the multipoint iterative methods with memory by addressing recent patents and scholarly articles on the constructing and application of the iterative method. Numerical experiments are used to demonstrate the efficiency and the performance of the multipoint iterative method. The results show that the multipoint iterative methods are particularly suitable for the high-precision computing.

Keywords: Computational efficiency, convergence order, multipoint iterative method, Newton type method, nonlinear equations, Steffensen type method.